Projection-based Control: A Novel Paradigm for High-performance Systems

Introduction

The field of control has been a key driver for major societal innovations in health, mobility, energy, and manufacturing. At present, technological trends push the performance requirements for future applications to extreme levels that are far beyond current control solutions.

Current Limitations

Existing linear controllers for linear systems are supported by user-friendly time- and frequency-domain design tools, yet they lack the flexibility to overcome fundamental performance trade-offs. Full nonlinear control structures provide the desirable flexibility, but they lack comprehensive frequency-domain design techniques.

These observations indicate a lack of flexible control structures accompanied by systematic design and online optimization frameworks that exploit time- and frequency-domain information to realize the unparalleled performance needs of future engineering systems.

Project Overview

In PROACTHIS, I will bridge this scientific gap by creating a new control paradigm based on projection operators. By introducing projections in control loops, specific signals are kept in well-chosen constraint sets, inducing direct performance-enhancing benefits.

Expected Outcomes

I foresee that the mathematical structure of these projection-based controllers enables fundamental properties that were instrumental in the success of linear control and will be key to obtaining effective design frameworks for this new class of hybrid controllers.

Challenges and Methodologies

Developing projection-based control theory has high risks, as even the mathematical formalization of these control schemes leads to a new class of dynamical systems never studied before. This scientific challenge calls for leveraging powerful multi-disciplinary methodologies from:

1. Hybrid Systems
2. Control Engineering
3. Networked Systems
4. Learning
5. Mathematics

Conclusion

Successfully developing this new system theory will pave the way towards game-changing cutting-edge control methodologies addressing the needs of future engineering systems, thereby enabling new breakthroughs in important societal domains.